Merge vertex to face
I'm not entirely sure I understand how you cylinders are aligned towards each other, but it doesn't matter to much. I'm going to use the "bridge two edgeloops" operation.

Here is my starting position:



I edit both of them and remove the end caps.



Then I select them both and join them Ctrl + J. Now I again go into edit mode and select both edgeloops at the end of the cylinders. Hold down Alt to select and edge loop. Hold down Shift + Alt to select the other without deselecting the first.

Then hit space and type "bri" in the menu. It should look like this. Hit Enter



Now the two edge loops should be bridged with faces: